Q: Given the matrices $$A = \begin{bmatrix} 1 & 2 \\ 3 & 4 \end{bmatrix}$$ and $$B = \begin{bmatrix} 2 & 0 \\ 1 & 2 \end{bmatrix}$$, what is $$A + B$$?

$$\begin{bmatrix} 3 & 2 \\ 4 & 6 \end{bmatrix}$$

Question 1

Which of the following relations is NOT a function?

Accepted Answer

A relation where the point $$(2, 5)$$ and $$(2, -3)$$ are both present.

Question 2

Given the function $$f(x) = 2x^2$ - 3x + 1$$, what is the value of $$f(-2)$$?

Accepted Answer

$$f(-2) = 15$$

Question 3

A company models its revenue $$R in $$thousands of dollars by the function $$R(x) = 5x + 20$$, where $$x is $$the number of units sold (in hundreds). What is the slope of the revenue function, and what does it represent?

Accepted Answer

Slope is $$5$$; it represents the revenue increase per additional hundred units sold.

Question 4

Which of the following equations represents a line perpendicular to $$y = -\frac{1}{2}x + 3$$?

Accepted Answer

$$y = 2x - 1$$

Question 5

If $$f(x) = x^2$ and g(x) = x + 1$, what is (f$$ \circ g)(2)$$?

Accepted Answer

$$(f \circ g)(2) = 9$$

Question 6

Which of the following describes the transformation of the graph of $$y = x^2$ to y$$ = $$(x-3)^2 + 2$?

Accepted Answer

Shift right 3 units and up 2 units.

Question 7

A quadratic function models the height $$h (in $$meters) of a ball thrown upward as $$h(t) = -4.9t^2$ + 20t + 1.5$$, where $$t is $$time in seconds. What is the maximum height reached by the ball?

Accepted Answer

$$h_{max} = 21.9$$ meters

Question 8

Which of the following is the inverse of the function $$f(x) = 3x - 7$$?

Accepted Answer

$$f^{-1}(x$$) = \frac{x+7}{3}$$

Question 9

Solve for $$x$$: $$2^{x} = 16$

Accepted Answer

$$x = 4$$

Question 10

Which of the following is equivalent to $$\log_{2} 32$$?

Accepted Answer

$$5$$

Question 11

A population of bacteria triples every 4 hours. If the initial population is 200, which function models the population $$P(t)$$ after $$t$$ hours?

Accepted Answer

$$P(t) = 200 \cdot 3$$^{t/4}$$

Question 12

Which of the following is the solution to the system of equations: $$\begin{cases} 2x + 3y = 7 \ x - y = 1 \end{cases}$$?

Accepted Answer

$$x = 2, y = 1$$

Question 13

Given the matrices $$A = \begin{bmatrix} 1 & 2 \ 3 & 4 \end{bmatrix}$$ and $$B = \begin{bmatrix} 2 & 0 \ 1 & 2 \end{bmatrix}$$, what is $$A + B$$?

Accepted Answer

$$\begin{bmatrix} 3 & 2 \ 4 & 6 \end{bmatrix}$$

Question 14

Which of the following is the domain of the function $$f(x) = \frac{1}{x-5}$$?

Accepted Answer

All real numbers except $$x = 5$$

Question 15

If $$f(x) = \sqrt{x-2}$$, what is the range of $$f(x)$$?

Accepted Answer

$$[0, \infty)$$

Question 16

Which of the following is a solution to the equation $$x^2 - 5x + 6 = 0$?

Accepted Answer

$$x = 2$$

Question 17

A car depreciates in value by 12% each year. If the initial value is $$V_0$$, which function models the value $$V(t)$$ after $$t$$ years?

Accepted Answer

$$V(t) = V_0$ \cdot (0.88)^t$$

Question 18

Which of the following is the sum of the first 5 terms of the arithmetic sequence $$a_n = 7 + 3(n-1)$$?

Accepted Answer

$$55$$

Question 19

If $$\log_{b} 81 = 4$$, what is the value of $$b$$?

Accepted Answer

$$b = 3$$

College Algebra Syllabus and Course Structure Overview

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